Highest Common Factor of 283, 176, 420 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 283, 176, 420 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 283, 176, 420 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 283, 176, 420 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 283, 176, 420 is 1.

HCF(283, 176, 420) = 1

HCF of 283, 176, 420 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 283, 176, 420 is 1.

Highest Common Factor of 283,176,420 using Euclid's algorithm

Highest Common Factor of 283,176,420 is 1

Step 1: Since 283 > 176, we apply the division lemma to 283 and 176, to get

283 = 176 x 1 + 107

Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 107 and 176, to get

176 = 107 x 1 + 69

Step 3: We consider the new divisor 107 and the new remainder 69, and apply the division lemma to get

107 = 69 x 1 + 38

We consider the new divisor 69 and the new remainder 38,and apply the division lemma to get

69 = 38 x 1 + 31

We consider the new divisor 38 and the new remainder 31,and apply the division lemma to get

38 = 31 x 1 + 7

We consider the new divisor 31 and the new remainder 7,and apply the division lemma to get

31 = 7 x 4 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 283 and 176 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(31,7) = HCF(38,31) = HCF(69,38) = HCF(107,69) = HCF(176,107) = HCF(283,176) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 420 > 1, we apply the division lemma to 420 and 1, to get

420 = 1 x 420 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 420 is 1

Notice that 1 = HCF(420,1) .

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Frequently Asked Questions on HCF of 283, 176, 420 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 283, 176, 420?

Answer: HCF of 283, 176, 420 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 283, 176, 420 using Euclid's Algorithm?

Answer: For arbitrary numbers 283, 176, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.